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    Graph energy ranking for scale-free networks using Barabasi-Albert model
    (Institute of Electrical and Electronics Engineers Inc., 2019) Mahadevi, S.; Kamath, S.S.
    A social network is a vast collection of actors and interactions. It forms one of the complex networks. There are various types of social networks such as acquaintance networks, online social networks, covert networks, citation networks, and collaboration networks, etc. Most of these real-world networks are scale-free, and they follow a power-law distribution. Each of these networks has nodes which have various roles to play, and all nodes are not equally important. Hence we need to rank them based on their importance. In this paper, we propose an algorithm named Graph Energy Ranking (GER) to rank the nodes of scale-free networks built using the Barabasi-Albert model. GER analyses the impact of node deletion on the underlying network and therefore gives a better understanding of the network features. Study of ranking done by existing centrality measures versus GER is performed to observe the similarity in the ranking process. ©2019 IEEE.
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    Graph energy centrality: a new centrality measurement based on graph energy to analyse social networks
    (Inderscience Publishers, 2022) Mahadevi, S.; Kamath, S.S.; Shetty D, P.D.
    Critical node identification, one of the key issues in social network analysis, is addressed in this article with the development of a new centrality metric termed graph energy centrality (GEC). The fundamental idea underlying this GEC measure is to give each vertex a centrality value based on the graph energy that results from vertex elimination. We show that the GEC of each vertex is asymptotically equal to two for cycle graphs and exactly equal to two for complete graphs. We further demonstrate that star graphs can be ranked using only two GEC values, whereas path graphs can be ranked using a maximum of ⌈n+12 ⌉ values. The proposed algorithm takes O(n3) time complexity to rank all vertices; hence an optimised algorithm is also being proposed considering only a few classes of graphs. The proposed algorithm ranks the nodes based on the collaborative measure of eigenvalues. © 2022 Inderscience Enterprises Ltd.. All rights reserved.